Explore hyperbolic and non-hyperbolic fixed points in dynamical systems and learn techniques for computing their invariant manifolds using Taylor series expansions. Delve into the stable, unstable, and center subspaces for discrete-time dynamical systems, and understand the significance of corresponding invariant manifolds in nonlinear settings. Examine a 2D example of analytically obtaining stable and unstable manifolds, and discover methods for approximating invariant manifolds. This lecture, part of a course on center manifolds, normal forms, and bifurcations, provides essential insights for students with a background in elementary analysis, multivariable calculus, and linear algebra.